McKean-Vlasov stochastic differential equations with super-linear measure arguments: well-posedness and propagation of chaos

TL;DR

This paper proves the well-posedness and propagation of chaos for McKean-Vlasov SDEs with super-linear growth in coefficients, using an Euler-like scheme and analyzing particle system convergence.

Contribution

It introduces new methods to establish strong solutions and chaos propagation for MVSDEs with super-linear measure and state-dependent coefficients.

Findings

Strong well-posedness under locally monotone conditions

Convergence of particle systems to non-interacting limits

Numerical simulations validating theoretical results

Abstract

This paper studies McKean-Vlasov stochastic differential equations (MVSDEs) whose drift coefficients grow super-linearly in both state variables and measure arguments, and whose diffusion coefficients exhibit super-linear growth in the state variables. By constructing an Euler-like sequence, we establish the strong well-posedness of such MVSDEs under a locally monotone condition. Furthermore, the propagation of chaos is studied on both finite and infinite horizons, demonstrating convergence of the interacting particle system to the corresponding non-interacting system. To illustrate the rationality of the theoretical results, we provide examples whose drifts contain the high powers and multiple integrals of distributions, with numerical simulations presented in Section 6.